If the mean of the numbers $27 + x$,$31 + x$,$89 + x$,$107 + x$,and $156 + x$ is $82$,then the mean of $130 + x$,$126 + x$,$68 + x$,$50 + x$,and $1 + x$ is:

If the mean of the first $n$ natural numbers is equal to $\frac{n + 7}{3}$,then what is the value of $n$?

The arithmetic mean of a set of observations is $\overline{X}$. If each observation is divided by $\alpha$ and then increased by $10$,then the mean of the new series is

$A$ school has four sections of chemistry in class $XII$ having $40, 35, 45$ and $42$ students. The mean marks obtained in chemistry test are $50, 60, 55$ and $45$ respectively for the four sections. The overall average of marks per student is:

What is the value of $x$ if the mean of $8, 6, 7, 5, x,$ and $4$ is $7$?

If in an examination different weights are assigned to different subjects: Physics $(2)$,Chemistry $(1)$,English $(1)$,and Mathematics $(2)$. If a student scored $60$ in Physics,$70$ in Chemistry,$70$ in English,and $80$ in Mathematics,then his weighted $A.M.$ is: